Channel estimation is often used to facilitate communications, such as to provide reliable decoding of data in a communication system. For example, wireless communications will often experience different channel responses in different environments and/or at different times, such as due to multi-path phenomena. It is therefore often desirable to estimate the channel response in order to establish high quality communications in the existing communication environment.
Multi-carrier communication systems, such as systems utilizing orthogonal frequency division multiplex (OFDM), which includes OFDM where the symbol is used by one user or multiple users (e.g., orthogonal frequency division multiple access (OFDMA)), often employ a pilot subcarrier to provide channel estimation with respect to data subcarriers used thereby. In OFDM and OFDMA systems, for example, where there are enough pilot subcarriers and the distribution of the pilot subcarriers is uniform and/or contiguous (consecutive), the channel response of the data subcarriers can be estimated relatively accurately from a measured pilot subcarrier channel response using the following relationship;Ĥt=AHP  (1)In the foregoing, Ĥt is the estimated channel response of subcarrier t, where t is an element of the set of all used subcarriers (T), Hp is the channel response of all pilot subcarriers, where P is a subset of T, and A is a filter matrix providing channel estimation.
The number of pilot subcarriers needed in each symbol in order for the foregoing relationship to provide an accurate estimation of the data subcarriers channel response depends upon the channel characteristics. This relationship can be represented as follows:
                                                        1                              S                p                                      >                          τ              max                                ,                                          ⁢                                    S              p                        -                          Pilot              ⁢                                                          ⁢              subcarrier              ⁢                                                          ⁢              spacing                                      ⁢                                  ⁢                              τ            max                    -                      maximum            ⁢                                                  ⁢            delay            ⁢                                                  ⁢            of            ⁢                                                  ⁢            the            ⁢                                                  ⁢            channel                                              (        2        )            In the foregoing, Sp is the pilot subcarrier spacing and τmax is the maximum delay of the channel.
From the above, it can be appreciated that unavailability of an appropriate number of pilot subcarriers (e.g., often an appreciable amount of the available spectrum) and/or long channel delays (e.g., channel delays longer than a cyclic preamble (CP)) can present challenges in accurately estimating the data subcarrier channel. Further exacerbating the problem is the fact that the pilot subcarriers may not be consecutive or uniformly distributed, as presumed in the fundamental relationship of equation (1). Specifically, in various communication systems the available pilot subcarriers may not be continuously and uniformly distributed, thus rendering a data subcarrier channel estimation based upon a measured pilot subcarrier channel response using the relationship of equation (1) inaccurate.
For example, OFDMA systems operable under the IEEE 802.16e standard utilize subcarriers grouped into a tile arrangement. In such a tile arrangement the pilot subcarriers are typically not contiguous (non-consecutive) and not uniformly distributed (spacing between some pilot subcarriers and their nearest neighbor pilot subcarriers is not consistent). Moreover, a tile may be placed far away from other tiles and thus the channel response of data subcarriers in a tile should only be estimated using pilot subcarriers within that tile. Such a configuration results in very poor data subcarrier channel estimation using the measured pilot channel response and the relationship of equation (1).